Authority fields have a number of options you can choose from. You can type in the term and the system will find the match from the available options. You can also press the Options buttonto bring up a list of options.
If you know the System ID of the term you can enter that as a shortcut.
If the term doesn't exist you can create new Authority terms.
Authority Assisted fields are text fields that also have options that you can choose from. You can freely enter text, or you can use the Options buttonto show available terms.